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u-substitution integral sin(pi*x) antiderivative using substitution to get integral of sin(pi*x).
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Integrate sin(pi*x) formally and informally using u substitution for sin(pi*x) or find sin(pi*x) antiderivative informally by using the chain rule backwards.
Antiderivative of sin(pi*x): we integrate sin(pi*x) using a u-substitution with u=pi*x. This means du=pi*dx, and we can formally replace dx with 1/pi*du. Alternatively, we can recognize the "chain rule backwards" and just set the integral up with an extra factor of pi inside, and a 1/pi outside, then guess the integral of sin(pi*x).
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